[or y= (3 - e^(2x))^(1/2)]
Here you should switch the x and y, and then solve for y. The result will give you the inverse. So instead of
y^2 = 3 - e^(2x)
you should have
x^2 = 3 - e^(2y)
... and so on.

As eumyang said, it is just a matter of notation. We typically write a function as "y= f(x)", not "x= f(y)". But, of course, as long as f is the same function "y= f(x)", "x= f(y)", or "b= f(a)" all refer to the same function.